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arXiv · 1403.0277

A space-time FEM for PDEs on evolving surfaces

Joerg Grande·Maxim Olshanskii·Arnold Reusken
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Abstract

The paper studies a finite element method for computing transport and diffusion along evolving surfaces. The method does not require a parametrization of a surface or an extension of a PDE from a surface into a bulk outer domain. The surface and its evolution may be given implicitly, e.g., as the solution of a level set equation. This approach naturally allows a surface to undergo topological changes and experience local geometric singularities. The numerical method uses space-time finite elements and is provably second order accurate. The paper reviews the method, error estimates and shows results for computing the diffusion of a surfactant on surfaces of two colliding droplets.

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Joerg Grande, Maxim Olshanskii, Arnold Reusken. 2014-03-02. A space-time FEM for PDEs on evolving surfaces. https://arxiv.org/abs/1403.0277

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